Manufacturers have frequently used statistical analysis to evaluate whether a product meets quality standards and can therefore be sold. The statistical analysis typically involves subjecting a product that is made of components to a test to determine whether the product passes the test. For example, a disk drive is made of many components, such as a read/write head, the pole tip of the read/write head, a platter, a head, etc. Each of these components have parameters that can be measured. For example, the recession of the pole tip and the strength of the magnetic signal generated by the read/write head (commonly referred to as “amplitude”) are a couple of examples of parameters of read/write heads that can be measured.
The test used in determining the quality of the product, such as a disk drive, could involve creating a set (e.g., population) of disk drives and testing the set of disk drives along many parameters to determine the quality of the disk drives. For example, in testing for amplitude and recession a population of read/write heads can be built from a single wafer to try and make the read/write heads as identical as possible. Then the read/write heads can be sorted into categories from lowest to highest according to the amount of recession associated with the pole tips of the read/write heads so that each category has approximately the same amount of recession. Then disk drives can be built using the categorized read/write heads and the disk drives can be tested. While performing the test, the amplitude, can be measured.
The values of the measurements can be used to perform statistical analysis. FIG. 1 depicts aspects of performing statistical analysis. More specifically FIG. 1 depicts two graphs 110, 120 and two equations 130, 140. The graph 110 has an axis for the amount of recession 114 associated with pole tips and a probability of failure 112. Each pole tip will have a particular amount of recession 114 that will result in a particular amount of amplitude and an associated probability of failure 112. The amount of recession 114 that results in a particular amount of amplitude and probability of failure 112 are graphed on graph 110 resulting in the curves AMP1, AMP2, AMP3. Graph 120 plots the probability of failure 122 that results from various amounts of amplitude 124. Since amplitude is inversely proportional to the amount of recession associated with a pole tip, graph depicts the curves of recession (REC1, REC2, REC3) that result from the various the values of recession associated with various degrees of amplitude.
The probability of failure 130 (e.g., Pf) is an equation that is used to evaluate the probability of components to fail a test, such as a functional test of a disk drive, based on various parameters that were measured, according to one embodiment. Equation 132 is a simplified representation of the equation 130 and equation 134 is an expanded representation of the equation 130. The expanded version 134 of the equation 130 is a polynomial. Further, the probabilities to fail for each of the components can be used to calculate an average probability to fail. For example, all of the probabilities of failure for all of the components can be averaged to calculate an average probability of fail using equation 140.
Although the equations 130, 132, 134 are shown using values for the recession and amplitude parameters, values for many parameters can be used in calculating the results of the equations. For example, all dimensions of the read/write heads as well as various electrical and magnetic properties can be used. The equations 130, 132, 134 are commonly referred to as the multiple variant model fitting which is used in modeling of product yield based on parametric data.
In order to stay competitive, manufacturers have to constantly try to provide better quality products while at the same time maintaining or even reducing costs. There may be a number of reasons that manufacturers may want to modify a parameter of a component. For example, they may want to make a less expensive version of the component or a certain parameter of the component may be difficult to measure. So they may want a version of the component where that parameter is easier to measure or where that parameter does not need to be measured at all.
In order to do this, manufacturers have to design new processes for manufacturing their products. For example, the manufacturer of a disk drive may want to improve one of the components, such as the pole tip, that goes into creating a disk drive. They may design a new process that they believe will improve a parameter of the pole tip, such as pole tip recession. However, in modifying the pole tip recession other parameters of the pole tip, such as amplitude, may also be affected. Thus, it is difficult to determine whether a product meets quality standards for sale after using these new processes to build components of the product.
Determining whether a product meets quality standards involves setting up a manufacturing environment for building the product, building a lot of the product, and testing a lot of the product, all of which is very time consuming and expensive. For these and other reasons, a method for evaluating processes for manufacturing components would be valuable without requiring the setup of the manufacturing environment to build a complete product, etc.